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Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and applications

Volume 240 / 2018

Vinícius V. Fávaro, Daniel Pellegrino Studia Mathematica 240 (2018), 123-145 MSC: Primary 46A20, 46G20, 46A16; Secondary 46G25, 47A16. DOI: 10.4064/sm8608-4-2017 Published online: 25 August 2017

Abstract

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasi-norms instead of norms. In this paper we extend a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the dual of the space with the new norm coincides with the dual of the space with the original quasi-norm. Applications to problems on the existence and approximation of solutions of convolution equations and on hypercyclic convolution operators on spaces of entire functions are provided.

Authors

  • Vinícius V. FávaroFaculdade de Matemática
    Universidade Federal de Uberlândia
    Uberlândia, MG, Cep: 38.400-902, Brazil
    e-mail
  • Daniel PellegrinoDepartamento de Matemática
    Universidade Federal da Paraíba
    João Pessoa, PB, Cep: 58.051-900, Brazil
    e-mail
    e-mail

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